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Chapter 8: Immune reactions to chronic viruses Theoretical - - PowerPoint PPT Presentation
Chapter 8: Immune reactions to chronic viruses Theoretical - - PowerPoint PPT Presentation
Chapter 8: Immune reactions to chronic viruses Theoretical Biology 2016 CD4 and CD8 T cells CD8 CD4 HIV life cycle Konstantinov Science 2011 CD4 + T cell From Campbell T cell help Immunity to HIV Cell-intrinsic antiviral immunity?
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HIV life cycle
From Campbell
Konstantinov Science 2011
CD4+ T cell
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NK cell B cell CD8+ CTL CD4+ T cell TH17 cell γδ T cell HIV-1-infected CD4+ T cell DC HIV-1 ? MHC class II MHC class I LILR TCR Peptide ? ? BCR KIR Integration of viral DNA into the host genome Cell-intrinsic antiviral immunity Cell-intrinsic antiviral immunity? Neutralization? Macrophage Cytolysis ER ADCC? ADCVI? ADCP? Cytolysis T cell help T cell help Cell-intrinsic antiviral immunity
- Walker & Yu, Nat Rev Imm 2013
Immunity to HIV
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Time course of an HIV infection
O’Brien & Hendrickson, Genome Biol. 2013
Slow decline of CD4+ T cells: AIDS due to loss of immunity Fairly stable viral setpoint for many years: time to AIDS
CD4 loss: 50-100 cells/year
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Viral load predicts rate of disease progression
From: Mellors et al. Science 1996 low V load high V load
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Immune response does not correlate with viral load
From: Novitsky et al. J
- Virol. 2003
Log viral load
Immune response to one protein
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Caricature scheme
T I E V
p δV δT δI δE k α β σ
CD4+ T cell Infected immune Effector
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Mathematical model
Set δI > δT to allow for cytopathic effects of the virus
dT dt = σ − δTT − βTV , dI dt = βTV − δII − kEI , dV dt = pI − δV V , dE dt = αEI − δEE .
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Steady state
¯ I = δE α ¯ V = p δV ¯ I = pδE αδV ¯ T = σ δT + β ¯ V = ασδV αδTδV + pβδE ¯ E = pβ kδV ¯ T − δI k = pβασ k(αδTδV + pβδE) − δI k
Only the rate at which immune cells are activated, α, determines the viral burden I.
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Viral load (V), targets (T) and immune response (E) as a function of activation parameter (α)
When α>0.01 the immune response hardly changes, but the viral load (V or I) changes markedly.
Patients having similar immune response can have very different viral loads!
What happens at α=10-4?
(a)
α ¯ V =
p δV ¯
I
10−5 10−4 10−3 10−2 0.1
1 1 10 104 105
(b)
α ¯ T
10−5 10−4 10−3 10−2 0.1
1 1 100 104
(c)
α ¯ E
10−5 10−4 10−3 10−2 0.1
1 0.5 1
¯ V = pδE αδV
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Viral load (V), targets (T) and immune response (E) as a function of activation parameter (α)
When α>0.01 the immune response hardly changes, but the viral load (V or I) changes markedly.
Patients having similar immune response can have very different viral loads!
Bifurcation at α=10-4: Immune response disappears
(a)
α ¯ V =
p δV ¯
I
10−5 10−4 10−3 10−2 0.1
1 1 10 104 105
(b)
α ¯ T
10−5 10−4 10−3 10−2 0.1
1 1 100 104
(c)
α ¯ E
10−5 10−4 10−3 10−2 0.1
1 0.5 1
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Immune response does not correlate with viral load
From: Novitsky et al. J
- Virol. 2003
Log viral load
Immune response to one protein
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20 40 60 80 100
Time in days
10
3
10
4
10
5
Viral load in blood
δ
Perturb the steady state by treatment (ART)
Treatment:
What can this downslope δ tell us?
Ho and Perelson, Nature 1995, Science 1998
δ
dT dt = σ − δTT − βTV , dI dt = βTV − δII − kEI , dV dt = pI − δV V , dE dt = αEI − δEE .
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Separation of time scales: QSSA
dT dt = σ δTT β⇤TI , dI dt = β⇤TI δII kEI , dE dt = αEI δEE ,
Setting dV/dt=0 we obtain V=(p/δV)I, i.e., V becomes proportional to I:
where β’=pβ/δV
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Separation of time scales: E=constant
dT dt = σ δTT β⇤TI , dI dt = β⇤TI δII kEI , dE dt = αEI δEE ,
Setting δ = δI + kE we obtain from
dT dt = σ δTT β⇤TI , dI dt = β⇤TI δI ,
which we have seen before and has one steady state:
¯ T = δ β⇤ and ¯ I = σ δ δT β⇤
20 40 60 80 100
Time in days
10
3
10
4
10
5
Viral load in blood
Immune effectors E
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Use this model to infer viral dynamics from data
Nature 1995
This paper changed the field: HIV-1 is not slow at all. Utterly simple model teaches us a new biology.
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dT dt = σ δTT β⇤TI , dI dt = β⇤TI δI ,
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Use model to infer viral dynamics from data
dI dt = β⇤TI δI ,
Famous papers: HIV is not slow but has a generation time of 1-2 days
I(t) = I(0)e−δt
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Employing the fitness R0
R0 = β⇤σ δTδ
¯ T = σ δTR0 = K R0 and ¯ I = σ δ
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